Mike Lyle wrote:
why wasn't I taught real maths as a kid?

I don't understand that either. I bet loads of 7-year olds would be
turned on by the idea of old Euler teaching himself by chalking on
gravestones, or the discovies of Srinivasa Ramanujan in basic
arithmetic. I suspect that the problem is that people are taught by
teachers, not mathematicians.

I had a similar experience with Chemistry. they spent 3 years teaching
me random reactions, then suddenly told us of old Dmitri Mendeleev and
his periodic table, which let you work out in advance how things might
react from other things you knew. Then when I thought I'd peeped
behind the curtain at last, it was 2 years before I found out about the
physics of electron orbitals, which was a closer look at why it worked.

It was as though I had to repeat, in my own lifetime, all the stumbling
through fog that mankind had done, before discovering the wonderful
inner secrets. Just telling us the underlying mechanism first was
somehow cheating.

So we are taught long division, or methods of multiplying fractions
parrot fashion, by people who learned them parrot fashion. Any kid
that gets a clue as to /why/ the method works, and adapts it for
themselves is not regarded as clever, but as wrong. "That's not the
way it is done", they are told. Never "This is how it works".

I was lucky. My father taught me to multiply by legitimate discard, I
met a student teacher when I was 8 who bothered to explain some of the
properties of 9, including why the digits of multiples of 9 add up to
9. But for the vast majority of people they never, ever, get to hear
any real maths at school - except Pythagoras' theorem. I can tell
tales based around that bit of maths that will keep you enthralled for
hours, and have seen people use it in the most extraordinary places.
But our kids plod through it without enthusiasm, becuse no-one ever
shows any enthusiasm when they are presenting it.

It's not just sad, it's a form of child abuse in my opinion. Failing
to tell them one of the most wonderful stories we have ever learned.